Did you ever start singing a pop song with a long introduction? You came in at the right time, but you didn’t count the beats. There were many clues along the way that told you when to sing. Maybe a rhythmic pattern or a chord sequence or a preparatory kick on a drum told you to sing. The clues may be subtle (or obvious) but somehow you felt the entrance.
On the other hand, in some songs a short pattern in the intro can be repeated many times without giving you any clue when to add the melody. Even worse, the pattern sometimes continues leaving you with a mild anxiety attack wondering if you’re in the right spot until the next chord change happens. It will be a “Whew or Oops” moment. I guess you should have done your homework and counted how many beats or patterns occurred before the singing comes in.
Actually both approaches are valid
Young students taking formal instruction are taught to recognize written note and rest values. This gives them structure and enables them to sight read music, especially in group settings.
Movement is a response to feel
If you’re dancing at a wedding or in a night club, you start to move when you feel the music. Alternatively, when dancers or cheerleaders are practicing on stage or in a gym, they will always hear “5,6,7,8” so they can all step off at the same time. In this case they both count AND feel the beat.
Many young people self teach themselves to play the guitar or other musical instruments and can reach great heights in the music world. Most say “I don’t know what I’m doing but it sure feels good.” Actually, I am jealous of these people because whenever they play, its all feel and comes from within. It took me years to break away from always interpreting the personality of the composer and instead, add my own feelings to a performance.
Which comes first, emotional feeling or intellectual counting?
Different settings can go either way. In the end, counting is very important for the actual performer coupled with feeling, but for those that respond to music, feeling is all consuming. There is no right answer to this question, but it’s important to be able to notice the difference and strive for feeling.
As my first private teacher always said: “Play it with feeling… just don’t feel bad!”